15 Answers
15

Correlations are notoriously unstable in financial time series - yet one of the most used concepts in quant finance because their is no good theoretical substitute for it. You could say theory is not working with it yet neither without it.

For example the concept is used for diversification of uncorrelated assets or for the modelling of credit default swaps (correlation of defaults). Unfortunately when you need it most (e.g. a crash) it just vanishes. This is one of the reasons that the financial crises started because the quants modeled the cds's with certain assumptions concerning default correlations - but when a regime shift happens this no longer works.

+1 This is a good one; a really abused statistic.
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ShaneFeb 5 '11 at 23:43

I remember reading somewhere a comment that seeking non correlation is a complete waste of time; you want all your strategies to be 100 % correlated to a exponentially rising equity curve.
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babelproofreaderFeb 8 '11 at 21:37

4

Actually, we can turn this argument on its head. We can profit from the fact that correlation vanishes during a crisis, by selling correlation to the street. Fact is because many retail investors don't want to choose specific assets in an asset class, they tend to buy baskets. Since they also want capital protection, they tend to buy options on those baskets. Writing these options takes the street short the correlation of the basket elements, and they're happy to pay up to buy it back at (usually expensive) levels, which is what many Hedge Fund traders do through dual binaries and such like.
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Thomas BrowneJun 4 '11 at 11:50

"because their is no good theoretical substitute for it" this isn't entirely true
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pyCthonDec 8 '11 at 3:12

2

@Jase: You are right, this was imprecise. I meant that it goes from uncorrelated or even negatively correlated to strongly correlated. So the "uncorrelatedness" vanishes.
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vonjdDec 14 '12 at 10:07

The CAPM, like Markowitz's (1952,
1959) portfolio model on which it is
built, is nevertheless a theoretical
tour de force. We continue to teach
the CAPM as an introduction to the
fundamental concepts of portfolio
theory and asset pricing, to be built
on by more complicated models like
Merton's (1973) ICAPM. But we also
warn students that despite its
seductive simplicity, the CAPM's
empirical problems probably invalidate
its use in applications.

Note that CAPM adds many assumptions to Markowitz's fundamental model to built itself. Therein lies its fallacy because as said above, those are difficult assumptions. Markowitz' model itself is fairly general in that you can inject 'views' of higher returns or greater volatility etc into the basic framework (or not!) and still be quite rooted in reality for mid-long term horizons.

I would contradict this by saying that one can say that the market is efficient or not even in the presence of transaction costs, irrational behavior or slow information diffusion. All you need is SOME rational investors, SOME spread of information and the ability for the Rationals to make money off the Irrationals. You can read more about it in the first chapter of Rebonato's "Volatility and Correlation" book.
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quant_devFeb 6 '11 at 16:19

@quant_dev I wasn't disputing market efficiency in general, but just that $\beta$ can be effectively used for allocation (in the traditional CAPM framework).
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ShaneFeb 6 '11 at 17:18

I don't think it's been shown to be violated. They've struggled to confirm any cross-sectional relationship but that doesn't mean that it's been shown to be violated.
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JaseNov 12 '12 at 16:51

The great idea to have systematic indicator for risk exposure but the problems arise when

it's used as main or single indicator without looking at other risks (e.g Credit risk or Liquidity risk). Emanuel Derman wrote about it recently in his blog:

But they (GS) did it not with a new formula or a single rule. They did it by being smart rather than doctrinaire. They were eclectic; they had limits on all sorts of exposures -- on VaR, on the fraction of a portfolio that hadn't been modified in a year ... There isn't a formula for avoiding future losses because there isn't one cause of future losses.

VaR becomes the purpose of risk management - not the situations when when losses exceed VaR

“An airbag that works all the time, except when you have a car accident.” (c) D.Einhorm

It's focused on managable risk in a normal situations with the assumption that tomorrow will be like today and yesterday and without taking rare events into account.

It becomes another parameter (like profit) that could be gamed (the same profit but with low risk).

And there are two exremely great articles about VaR among the best I've ever read:

For many reasons. First, many adherents and critics support it for the wrong (often ideological) reasons. This applies even to well-known economists like John Quiggin. Second, because even fewer people know the extent and scope of the anomalies. The literature can get very technical. So even smart people rejecting the EMH, or publishing anomalies, end up being over-optimistic about their ability to beat the market.

Oops. No. Not only is the efficient market hypothesis supported by all the evidence, it is pretty difficult to argue that it has ever caused anywhere near as much trouble as those people who thought they could beat the market.
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user212Feb 7 '11 at 22:17

@user212 I get paid because of short-term inefficiencies in the market.
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chrisaycockFeb 8 '11 at 1:39

7

Published evidence. Anyone can claim otherwise, but you have to prove it, and right now no-one has proved they can beat the market by skill and not luck. Personally, I think it is probably unprovable, but this doesn't stop the EMH being useful. I won't go into details because it isn't relevant to my point: assuming the EMH is basically right hasn't caused anywhere near as much trouble as assuming it is basically wrong.
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user212Feb 17 '11 at 1:14

4

"Assuming the EMH is basically right hasn't caused anywhere near as much trouble as assuming it is basically wrong". I like that.
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quant_devMar 19 '11 at 17:41

I my opinion delta hedging is also a dangerous one, but it definitely should teach though. In the BS framework, it is an allegedly perfect way of covering the risk incurred by buying (or selling) a derivative product (such as call and put in simplest cases). Nevertheless due to several real world facts this doesn't work that well in practice :

discrete time rebalancing of porfolio

constant volatility so much things have been said on this I won't comment any further

Well, all the other tools in credit are worse. And copulas are VERY useful in FX/equity when pricing structured products.
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quant_devMar 19 '11 at 17:42

like all other models you just have to know when they work and when they don't
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pyCthonDec 8 '11 at 3:15

1

What didn't you like about the Wired article? It made a complex subject quite readable I thought; were their any factual errors, or was it just too dumbed down for your taste? (Incidentally the T. Mikosch paper was published Nov 2005; he must have felt vindicated come 2008 :-)
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Darren CookFeb 9 '12 at 1:48

Yes, it is vague, but I think it is really the root of all the problems that have been listed. People forgot that CAPM is a silly model and started to believe it. People forgot that risk has more than one dimension and started to believe VaR (and didn't question why it was necessary to give only one number to the people who really had the power).
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Patrick BurnsFeb 8 '11 at 11:06

Concepts must be based on logical ideas and proper premises. It is easy to forget a premise and then misuse a model such as CAPM as asset-allocation method as suggested by Shane so Y-Recheck-things. Do not make things personal. Do not abuse models with too complicated schemes (you may abuse some basic assumption) -- and even then don't expect pretend to know, rather to engineer.

That value stocks are necessarily riskier than growth; that there has to be a hidden risk factor that we haven't yet found. The Lakonishok, Shleifer, and Vishny abstract says it better than I can:

For many years, stock market analysts have argued that value strategies outperform the market. These value strategies call for buying stocks that have low prices relative to earnings, dividends, book assets, or other measures of fundamental value. While there is some agreement that value strategies produce higher returns, the interpretation of why they do so is more controversial. This paper provides evidence that value strategies yield higher returns because these strategies exploit the mistakes of the typical investor and not because these strategies are fundamentally riskier.

It is dangerous when large proportions of the trading population "religiously" believe [as a matter of unexamined faith] that certain necessary assumptions which govern the accuracy of the models they use will always hold. It is best to really understand how the models have been derived and to have a skeptics understanding of these assumptions and their impact. All models have flaws -- yet it is possible to use flawed models if you can get consistent indicators from several different or contrarian approaches based upon radically different assumptions. When the valuations from different approaches diverge, it is necessary to understand why -- when this happens, it is necessary to investigate the underlying assumptions ... this sort of environment often provides trading opportunities, but the environment can also quite easily be an opportunity for disaster.

Of course, implicit and explicit assumptions are absolutely necessary to sufficiently simplify any mathematical analysis and to make it possible to derive models that can give lots of traders the generally useful trading "yardsticks" that they rely upon. As an example, consider the Black-Scholes model. The Black-Scholes model is ubiquitous; a commonly used "yardstick" for option valuations. The Black-Scholes model of the market for a particular equity explicitly assumes that the stock price follows a geometric Brownian motion with constant drift and volatility.

This assumption of "geometric Brownian motion with constant drift and volatility" is never exactly true in the very strictest sense but, most of the time, it is a very useful, simplifying assumption because stock prices are often "like" this. It might not be reality, but the assumption is a close enough approximation of reality. This assumption is highly useful because of how makes it possible to apply stochastic partial differential equations methodology to the problem of determining appropriate option valuations. However, the assumption of "constant drift and volatility" is a very dangerous assumption in times when judgement, wisdom and intuition would tell an experienced investor "Something is "odd." It's as if we're in the calm before the storm." OR "Crowd psychology and momentum seem to be more palpable factor in the prices right now."

Black-Scholes derivation of the option pricing formula [per their original paper in JPE, v81] uses the assumptions of constant drift in stock price and volatility. In practice, everyone uses the freshest, most current, most recent estimates of drift and volatility every time that they use Black-Scholes ...that estimate is a constant, not a function of something ... the estimates are updated and the pricing formula gives a new answer ... but the formula's derivation is based upon drift and volatilty being constant over time, not varying with stock prices, stock price changes or anything else.
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markbrunsFeb 7 '11 at 22:16

1

This estimate is a function of time in the future. You re-estimate this function each day, as you said.
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quant_devFeb 8 '11 at 8:22

1

Yes ... the estimate that is redone every day is based upon an estimate of stock price drift constant and a stock price volatility constant. Black-Scholes estimates might still be quite useful, but should be taken with a grain of salt if new information was available that indicated stock price drift or volatility were going to change over time (e.g. expiration of a significant patents plus failure of replacement next generation patents; new election showing relevance of significant political pressure for change in government regulation affecting a company where rules were not yet written).
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markbrunsFeb 8 '11 at 15:38

That is to say, both the models and psychology tend to ignore the possibility of such behavior as takeovers, spinouts, significant changes in leverage (ratio of debt to equity) by issuing or redeeming bonds, and the like.

Now, there are desks (such as merger arb) that specifically play these, and fundamental analysts discuss and sometimes "model" them (if you can call their relatively simple spreadsheets models). But you'll find that the difficulty of including them in options models keeps them unincorporated, and plenty of traders fail to make the necessary mental adjustments.

Persistent autocorrelations in volatility processes are due to long term memory only. I cannot help but sigh at the hundreds of papers which work under this assumption. Haven't people heard about regime shifts?